I'm not sure how your scenario is really a probable one.
First, Guinan's line about 43 billion casualties is in reference to the entire war. Presumably this includes Klingon as well as Federation casualties. It's a figure from nearly 20 years of fighting, which the characters repeatedly refer to as being the case. Now they might be exaggerating, but it's clear the conflict had been waging for a long while, certainly longer than the career of NCC-1701-D. (Stated to be 4 years in service at this point.)
Second, if the Klingons had managed to so thoroughly route the Federation early, there's very little likelihood that the conflict could drag on for 20 years, much less allow the Federation to construct brand new and gigantic starships like the Enterprise
. We also know that technology progressed in those two decades to the point where the Galaxy
-class had a substantial superiority to the Ambassador
and that Picard's warship Enterprise
could have easily destroyed the 4 warbirds attacking Narendra III. That's not a state that got knocked out easily in the first few years of the war. If anything that's a state fighting total war for a long, long time in a conflict of attrition.
The Federation's tactical training by 2366 was evidently far superior to anything taught in the 2330s/2340s, assuming Castillo wasn't just humoring Yar to flirt with her. But at the same time, the Federation's tactical abilities (Or at least Garrett's) were sufficient to survive a four to one odds battle against Romulan warships sufficiently long enough for both the Klingons and the Federation to know what had happened to Narendra III.
We also know that the Klingons and Cardassians had fought an 18 year war at some point before 2370 (from the Betreka Nebula Incident). Noting for the record here that the Cardassians at least into the 2360s were not a "Great Power" like the Federation of the time, and their ships weren't as powerful. We know that an unshielded Nebula
configured for something other than battle (Phoenix
) could destroy a Cardassian warship (presumably a Galor
given its crew compliment of 600) with relative ease. Yet the Klingons weren't able to conquer them or even meaningfully defeat them over the course of an 18 year war. This gives us some idea of the relative capabilities of the Klingon Empire in the era preceding TNG.
We also know that the Federation had a fair share of conflicts in the early-mid 24th century. The ones we've heard as "wars" were with the Cardassians and Tzenkethi, and a series of border conflicts with the Talarians. We also know that the Tholians had destroyed a number of Federation outposts, like what happened with Kyle Riker.
Further, even if large parts of the fleet active circa 2293 was mothballed after the Khitomer Conference, we know that Starfleet was given sufficient resources to go around building new upgrades of the Excelsior
class. We know that they go from decommissioning Enterprise-A
somewhere around Stardate 9529.1 and launching Enterprise-B
on 9715.5. (Anywhere between a couple months and a couple years).
By the 24th century we're treated to dozens upon dozens of Excelsior
-class ships which were "top of the line" circa TUC. So even if a portion of the older ships were mothballed, Starfleet had more than made up for their loss by the 2320s-2340s. They had also commissioned substantially larger ships like the Ambassador
-class ships which were as much a boost in size over Excelsior
was over Enterprise
Finally Yar in "Yesterday's Enterprise" seems to know a LOT about the capabilities of Romulan ships, giving Castillo a thorough overview of what they need to do to actually defeat the 4 Romulan ships. Given that Starfleet in the "standard" timeline had no extensive contact with Romulans from 2311 to 2364,so there's SOMETHING that gave them substantial knowledge on Romulan tactical capabilities by 2366 in the altered timeline. An expanded war where everyone from the Cardassians, Tzenkethi, Sheliak, Talarians, Tholians, and Romulans were taking shots at the Federation sounds more likely as a way for them to be ground down over 20 years.